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simplificar (a^2-6a+9)/(a^2-1)*(-2a+2)/(2a-6)

Solución

simplificar

\frac{a ^{2} - 6 a + 9}{a ^{2} - 1} \cdot \frac{- 2 a + 2}{2 a - 6}

\frac{- a + 3}{a + 1}

Pasos de solución

\frac{a ^{2} - 6 a + 9}{a ^{2} - 1} \cdot \frac{- 2 a + 2}{2 a - 6}

Cancelar

\frac{- 2 a + 2}{2 a - 6} : \frac{- a + 1}{a - 3}

= \frac{a ^{2} - 6 a + 9}{a ^{2} - 1} \cdot \frac{- a + 1}{a - 3}

Aplicar las propiedades de las fracciones:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{( a ^{2} - 6 a + 9 ) ( - a + 1 )}{( a ^{2} - 1 ) ( a - 3 )}

Factorizar

a^{2} - 6 a + 9 : (a - 3)^{2}

= \frac{( a - 3 ) ^{2} ( - a + 1 )}{( a ^{2} - 1 ) ( a - 3 )}

Aplicar las leyes de los exponentes:

a^{b + c} = a^{b} \cdot a^{c}

(a - 3)^{2} = (a - 3) (a - 3)

= \frac{( a - 3 ) ( a - 3 ) ( - a + 1 )}{( a ^{2} - 1 ) ( a - 3 )}

Eliminar los terminos comunes:

a - 3

= \frac{( a - 3 ) ( - a + 1 )}{a ^{2} - 1}

Factorizar

a^{2} - 1 : (a + 1) (a - 1)

= \frac{( a - 3 ) ( - a + 1 )}{( a + 1 ) ( a - 1 )}

(a - 3) (- a + 1) = - (a - 3) (a - 1)

= \frac{- ( a - 3 ) ( a - 1 )}{( a + 1 ) ( a - 1 )}

Eliminar los terminos comunes:

a - 1

= \frac{- ( a - 3 )}{a + 1}

Poner los parentesis utilizando:

- (a - b) = - a + b

- (a - 3) = - a + 3

= \frac{- a + 3}{a + 1}

2 x^{3} + 3 x^{2} - 5 x - 6

\frac{100}{120}

\frac{\frac{x + y}{6}}{\frac{x ^{2} - y ^{2}}{3}}

\frac{5}{2} \div \frac{5}{7}

3 \times 1 0^{- 4}